Transfer Function Noise Research Articles

Drivers of barrier island water-table fluctuations and groundwater salinization

Barrier islands are threatened by climate change as sea-level rise and higher frequency storm surge lead to more flooding and saltwater intrusion. Vegetation plays a vital role in preventing erosion of barrier islands due to aeolian and hydrological forces. However, vegetation on barrier islands is threatened by rising water tables causing hypoxic conditions and storm-surge overwash introducing saline water to the root zone. To better protect barrier island ecosystems, it is critical to identify the relative influence of different hydrological drivers on water table elevation and salinity, and understand how this influence varies spatially and temporally. In this study, three barrier island sites were instrumented with groundwater wells monitoring water level and specific conductance. Using these data, a set of transfer function noise models were calibrated and used to determine the relative influence of hydrologic drivers including precipitation, evapotranspiration, bay and ocean water levels, and wave height on groundwater levels and specific conductance. We found that drivers of water-level change and specific conductance vary strongly among sites, depending primarily on the surface water connectivity and the geology of the island. Sites with close connection to inlets showed more salinization and responded to a larger number of drivers, while sites that were poorly connected to the ocean responded to fewer drivers.

Quantifying the natural flood management potential of leaky dams in upland catchments, Part I: A data-based modelling approach

A novel application of data-based time series methods is proposed in this study to help overcome barriers to quantifying the impacts of Natural Flood Management measures from hydrological timeseries data which hitherto have prevented accurate assessment of the effectiveness of interventions. To demonstrate the value of this method, a transfer function noise model was fitted to stage data from a three year before-after-control-impact style monitoring study of leaky dams in an upland catchment in North Yorkshire, England. Using the data-based time series method, uncertainties associated with stage data were overcome. The models were able to simulate the peaks of flood events on one stream to within ±2 cm accuracy for 95% of events recorded during the baseline monitoring period. These simulations are used in this study’s companion paper to quantify leaky dam impacts on flood peak magnitude. The level of accuracy achieved in this study provides proof of concept for application of the approach to data from other environments and natural flood management interventions, which is crucial if natural flood management is to be used as a mainstream flood risk management measure.

Quantifying the natural flood management potential of leaky dams in upland catchments, Part II: Leaky dam impacts on flood peak magnitude

Leaky dams are an increasingly popular natural flood management measure, yet their impacts on flood peak magnitude have not yet been empirically quantified for a range of event types and magnitudes, even at the stream scale. In this study, the novel application of a transfer function noise modelling approach to empirical Before-After-Control-Impact stage data from an upland catchment allowed leaky dam effectiveness in reducing flood peak magnitude to be quantified. Flood peak stage and discharge magnitude changes were assessed from empirical data for 50 single and multi-peaked high flow events with return periods ranging from less than one year to six years. Overall, event peak magnitude was significantly reduced following the installation of eight leaky dams on the impact stream. Effectiveness was highly variable, but on average, flood peak magnitude was reduced by 10% for events with a return period up to one year. Some of the variability was explained by the size of the event and whether it was a single or multi-peaked event. This finding emphasises the need to manage expectations by considering both a range of event magnitudes and types when designing or assessing leaky dam natural flood management schemes.

A data-driven approach for modelling Karst spring discharge using transfer function noise models

Karst aquifers are important sources of fresh water on a global scale. The hydrological modelling of karst spring discharge, however, still poses a challenge. In this study we apply a transfer function noise (TFN) model in combination with a bucket-type recharge model to simulate karst spring discharge. The application of the noise model for the residual series has the advantage that it is more consistent with assumptions for optimization such as homoscedasticity and independence. In an earlier hydrological modeling study, named Karst Modeling Challenge (KMC; Jeannin et al., J Hydrol 600:126–508, 2021), several modelling approaches were compared for the Milandre Karst System in Switzerland. This serves as a benchmark and we apply the TFN model to KMC data, subsequently comparing the results to other models. Using different data-model-combinations, the most promising data-model-combination is identified in a three-step least-squares calibration. To quantify uncertainty, the Bayesian approach of Markov-chain Monte Carlo (MCMC) sampling is subsequently used with uniform priors for the previously identified best data-model combination. The MCMC maximum likelihood solution is used to simulate spring discharge for a previously unseen testing period, indicating a superior performance compared to all other models in the KMC. It is found that the model gives a physically feasible representation of the system, which is supported by field measurements. While the TFN model simulated rising limbs and flood recession especially well, medium and baseflow conditions were not represented as accurately. The TFN approach poses a well-performing data-driven alternative to other approaches that should be considered in future studies.

Evaluating recharge estimates based on groundwater head from different lumped models in Europe

Study regionThe study uses 78 groundwater head time series across 10 European countries with various geological and hydrological settings. Study focusThe estimation of groundwater recharge using time series analysis and lumped modelling based on groundwater head time series is a low-cost and practical method. However, lumped recharge estimation models based on groundwater level variations are uncertain, and successful applications are known to depend on both climate and hydrogeological setting. Here, we assess the suitability of three different models to estimate recharge (Metran - Transfer Function-Noise model, AquiMod - groundwater level driven hydrological model, and GARDÉNIA - lumped catchment model). New hydrological insightsResults showed that while all three models generally did well during the modelling of groundwater heads, the resulting recharge estimations from the models were different. The analysis showed that the transfer-noise modelling of groundwater heads with recharge and evapotranspiration in Metran is not generally applicable for recharge estimation. The addition of physical information in AquiMod improved the recharge estimations, but the reliability was still limited without control of the water balance due to non-uniqueness. By adding discharge information to the modelling, GARDÉNIA can provide more reliable recharge values. Thus, recharge estimation from groundwater head time series without water balance information must be considered uncertain with low precision, but applicability can be improved when including knowledge of the local system.

Integration of observed and model-derived groundwater levels in landslide threshold models in Rwanda

Abstract. The incorporation of specific regional hydrological characteristics in empirical statistical landslide threshold models has considerable potential to improve the quality of landslide predictions towards reliable early warning systems. The objective of this research was to test the value of regional groundwater level information, as a proxy for water storage fluctuations, to improve regional landslide predictions with empirical models based on the concept of threshold levels. Specifically, we investigated (i) the use of a data-driven time series approach to model the regional groundwater levels based on short duration monitoring observations and (ii) the predictive power of single variable and bilinear threshold landslide prediction models derived from groundwater levels and precipitation. Based on statistical measures of the model fit (R2 and RMSE), the groundwater level dynamics estimated by the transfer function noise time series model are broadly consistent with the observed groundwater levels. The single variable threshold models derived from groundwater levels exhibited the highest landslide prediction power with 82 %–93 % of true positive alarms despite the quite high rate of false alarms with about 26 %–38 %. The further combination as bilinear threshold models reduced the rate of false alarms by about 18 %–28 % at the expense of reduced true alarms by about 9 %–29 % and is thus less advantageous than single variable threshold models. In contrast to precipitation-based thresholds, relying on threshold models exclusively defined using hydrological variables such as groundwater can lead to improved landslide predictions due to their implicit consideration of long-term antecedent conditions until the day of landslide occurrence.

An application of transfer function noise models for predicting groundwater level signals using rainfall signals in Adyar Basin, India

The effect of rainfall on groundwater level fluctuation was analysed using autoregressive moving average exogeneous (ARMAX) transfer function noise (TFN) modelling approach on four selected observation wells in Adyar Basin, Tamil Nadu, India. The evaluation of spatial average rainfall representation in the rainfall-groundwater level rise regression analysis was compared with three different methods namely simple arithmetic average (SAA), Thiessen polygon (TP), and Thiessen zone wise rainfall (TZR). Linear regression analysis on rainfall-groundwater level rise datasets revealed that the TZR method of inputting spatial average rainfall improved the rainfall-groundwater level rise correlation over SAA and TP methods. The four selected wells groundwater level fluctuation data from Adyar Basin was further modelled using ARMAX-TFN modelling approach and MLR methods. The study results show that the ARMAX-TFN model prediction performance was superior over MLR methods at all four locations. The validation results of the ARMAX-TFN model show that the predicted and observed groundwater levels at the corresponding well locations were strongly correlated with the correlation coefficient values of 0.85-0.93.

An application of transfer function noise models for predicting groundwater level signals using rainfall signals in Adyar Basin, India

An application of transfer function noise models for predicting groundwater level signals using rainfall signals in Adyar Basin, India

Estimation of groundwater recharge from groundwater levels using nonlinear transfer function noise models and comparison to lysimeter data

Abstract. The estimation of groundwater recharge is of paramount importance to assess the sustainability of groundwater use in aquifers around the world. Estimation of the recharge flux, however, remains notoriously difficult. In this study the application of nonlinear transfer function noise (TFN) models using impulse response functions is explored to simulate groundwater levels and estimate groundwater recharge. A nonlinear root zone model that simulates recharge is developed and implemented in a TFN model and is compared to a more commonly used linear recharge model. An additional novel aspect of this study is the use of an autoregressive–moving-average noise model so that the remaining noise fulfills the statistical conditions to reliably estimate parameter uncertainties and compute the confidence intervals of the recharge estimates. The models are calibrated on groundwater-level data observed at the Wagna hydrological research station in the southeastern part of Austria. The nonlinear model improves the simulation of groundwater levels compared to the linear model. The annual recharge rates estimated with the nonlinear model are comparable to the average seepage rates observed with two lysimeters. The recharges estimates from the nonlinear model are also in reasonably good agreement with the lysimeter data at the smaller timescale of recharge per 10 d. This is an improvement over previous studies that used comparable methods but only reported annual recharge rates. The presented framework requires limited input data (precipitation, potential evaporation, and groundwater levels) and can easily be extended to support applications in different hydrogeological settings than those presented here.

A transfer function modelling of Nigerian current account (Net) and exchange rate

This study proposes a transfer function noise model for the Nigerian current account (net) using the US dollar exchange rate as the input variable. The sixty annually collected time series data used covering the period 1960-2019 were obtained from the National Bureau of Statistics. Both series were non-stationary and were transformed by differencing. The transformed series were confirmed stationary using an appropriate test, the augmented Dickey-Fuller test, ADF. The cross-correlation function method was used for the estimation of the transfer model while the Box-Jenkins autoregressive integrated moving average method was used to separately model the autocorrelated noise term. The estimated transfer function with a noise model was subjected to a diagnostic check. The calculated Q-statistic offered evidence for the adequacy of the estimated model. For parsimony, estimates for the model parameters were recursively obtained after factorization.

Applying transfer function-noise modelling to characterize soil moisture dynamics: a data-driven approach using remote sensing data

The increasing availability of remotely sensed soil moisture data offers new opportunities for data-driven modelling approaches as alternatives for process-based modelling. This study presents the applicability of transfer function-noise (TFN) modelling for predicting unsaturated zone conditions. The TFN models are calibrated using SMAP L3 Enhanced surface soil moisture data. We found that soil moisture conditions are accurately represented by TFN models when exponential functions are used to define impulse-response functions. A sensitivity analysis showed the importance of using a calibrated period which is representative of the hydrological conditions for which the TFN model will be applied. The IR function parameters provide valuable information on water system characteristics, such as the total response and the response times of soil moisture to precipitation and evapotranspiration. Finally, we encourage exploring the possibilities of TFN soil moisture modelling, as predicting soil moisture conditions is promising for operational settings.

Spatial variation of groundwater response to multiple drivers in a depleting alluvial aquifer system, northwestern India

Unsustainable exploitation of groundwater in northwestern India has led to extreme but spatially variable depletion of the alluvial aquifer system in the region. Mitigation and management of groundwater resources require an understanding of the drivers behind the pattern and magnitude of groundwater depletion, but a regional perspective on these drivers has been lacking. The objectives of this study are to (1) understand the extent to which the observed pattern of groundwater level change can be explained by the drivers of precipitation, potential evapotranspiration, abstraction, and canal irrigation, and (2) understand how the impacts of these drivers may vary depending on the underlying geological heterogeneity of the system. We used a transfer function-noise (TFN) time series approach to quantify the effect of the various driver components in the period 1974–2010, based on predefined impulse response functions ( θ). The dynamic response to abstraction, summarized by the zeroth moment of the response M0, is spatially variable but is generally large across the proximal and middle parts of the study area, particularly where abstraction is high but alluvial aquifer bodies are less abundant. In contrast, the precipitation response is rapid and fairly uniform across the study area. At larger distances from the Himalayan front, observed groundwater level rise can be explained predominantly by canal irrigation. We conclude that the geological heterogeneity of the aquifer system, which is imposed by the geomorphic setting, affects the response of the aquifer system to the imposed drivers. This heterogeneity thus provides a useful framework that can guide mitigation efforts; for example, efforts to decrease abstraction rates should be focused on areas with thinner and less abundant aquifer bodies.

On the Influence of Transfer Function Noise on Sound Zone Control in a Room

Sound zones are valuable in scenarios where multiple people are present in the same room but want to listen to individual audio content without wearing headphones. The purpose of sound zone methods is to minimize the acoustic leakage between the zones by controlling multiple loudspeakers. This requires knowledge of how the loudspeakers interact with the room and radiate sound to the zones. That interaction is characterized by the transfer functions between the loudspeakers and microphones sampling the sound field in the zones. In this paper, the effect on the acoustic separation due to inherent noise in in situ transfer function measurements is investigated. The attainable separation is analyzed in the frequency range 20–300 Hz by means of the eigenfunctions of a rectangular room. The concept of observable degrees of freedom is introduced to indicate the number of active eigenfunctions, which are different within the zones at a given frequency. Likewise, controllable degrees of freedom indicate whether each source can excite the active eigenfunctions independently. It is argued that high separation can be achieved when the observable degrees of freedom are fewer than the controllable, and the target sound field can be described by the observable degrees of freedom. However, to attain this high separation it is a requirement that the details in the transfer functions associated with these degrees of freedom can be resolved in the presence of the measurement noise. For both simulated and experimental conditions the transfer functions are estimated using Bayesian inference and the uncertainty in the estimates is used to automatically regularize the sound field control. This regularization is seen to improve the performance when the measurement noise is correlated between the microphones and have little effect when the noise is uncorrelated.

Pastas: Open Source Software for the Analysis of Groundwater Time Series.

Time series analysis is an increasingly popular method to analyze heads measured in an observation well. Common applications include the quantification of the effect of different stresses (rainfall, pumping, etc.), and the detection of trends and outliers. Pastas is a new and open source Python package for the analysis of hydrogeological time series. The objective of Pastas is twofold: to provide a scientific framework to develop and test new methods, and to provide a reliable ready‐to‐use software tool for groundwater practitioners. Transfer function noise modeling is applied using predefined response functions. For example, the head response to rainfall is simulated through the convolution of measured rainfall with a Gamma response function. Pastas models are created and analyzed through scripts, ensuring reproducibility and providing a transparent report of the entire modeling process. A Pastas model can be constructed in seven simple steps: import Pastas, read the time series, create a model, specify the stresses and the types of response functions, estimate the model parameters, visualize output, and analyze the results. These seven steps, including the corresponding Python code, are applied to investigate how rainfall and reference evaporation can explain measured heads in an observation well in Kingstown, Rhode Island, USA. The second example demonstrates the use of scripts to analyze a large number of observation wells in batch to estimate the extent of the drawdown caused by a well field in the Netherlands. Pastas is free and open source software available under the MIT‐license at http://github.com/pastas/pastas.

Evaluating the impact of health awareness events on Google search frequency.

Over two hundred health awareness events take place in the United States in order to educate the public about various diseases. It would be informative and instructive for the organizations to know the impact of these events, although such information could be difficult to measure. We investigated whether 46 selected events attract the public attention by increasing the search frequencies of certain keywords. Internet search data from 2004 to 2017 were downloaded from Google Trend (GT). Three statistical methods including Transfer Function Noise modeling, Wilcoxon Rank Sum test, and Binomial inference were conducted. Our study showed that 10 health awareness events resulted in increased search frequencies in the event months, and 28 events did not, with the rest being classified as unclear.

Three Approaches to Time Series Forecasting of Petroleum Demand in OECD Countries

Petroleum (crude oil) is one of the most important resources of energy and its demand and consumption is growing while it is a non-renewable energy resource. Hence forecasting of its demand is necessary to plan appropriate strategies for managing future requirements. In this paper, three types of time series methods including univariate Seasonal ARIMA, Winters forecasting and Transfer Function-noise (TF) models are used to forecast the petroleum demand in OECD countries. To do this, we use the demand data from January 2001 to September 2010 and hold out data from October 2009 to September 2010 to test the sufficiency of the forecasts. For the TF model, OECD petroleum demand is modeled as a function of their GDP. We compare the root mean square error (RMSE) of the fitted models and check what percentage of the testing data is covered by the confidence intervals (C.I.). Accordingly we conclude that Transfer Function model demonstrates a better forecasting performance.

Statistical Interpolation of Groundwater Hydrographs

AbstractGroundwater observation bores are often monitored irregularly and infrequently. The resulting groundwater hydrographs are consequently less informative for understanding groundwater level trends, seasonality, flow directions, drawdown, and recovery. This paper presents an approach to temporally interpolate a groundwater hydrograph that has an irregular observation frequency to daily time steps. The approach combines nonlinear transfer function noise modeling with temporal kriging of the model residuals to produce an interpolated hydrograph that honors all water level observations input to the modeling and accounts for meteorological forcing between the observations. The reliability of the approach was evaluated using six observation bores having extended periods of daily data and by resampling them to six observation frequencies ranging from weekly to annually. The analysis showed that for weekly to monthly resampled data, >90% of the observed daily variability can be simulated at four of six bores. The performance declined with observation step size, as expected, but even at a biannual time step the error corrected interpolation can explain >70% of the variance at three of six bores. Additionally, an application shows that (1) the probability of a water level depth being exceeded can be estimated from quarterly resampled data and (2) the median annual water level range can be estimated from monthly resampled data. Supplementing less frequent observations with 6 and 12 months of daily data was also examined, with the addition of a 12‐month period significantly improving interpolation results at three of the four analyzed bores. The approach has been incorporated into the HydroSight toolbox http://peterson‐tim‐j.github.io/HydroSight/.

Transfer Function-Noise Modeling of the Dynamic Relationship between Botswana's Monthly Maximum Temperature and Evaporation

In Botswana, the rate of evaporation over open water surfaces is high because the country is characterised by hot and semi arid climatic conditions. The purpose of the study is to investigate the correlation between Botswana's monthly maximum temperature and evaporation and between monthly maximum wind speed and evaporation, for the stations Gaborone, Francistown and Maun and to fit transfer function-noise models between the highly correlated elements. The data were obtained from the Botswana Department of Meteorological Services. Cross correlation analysis revealed that for the selected weather stations, monthly maximum evaporation is much more strongly correlated to monthly maximum temperature than to monthly maximum wind speed. Monthly maximum temperature and evaporation were modelled with transfer function-noise models. The results of the study are crucial mainly to those in water management, agriculture and other similar industries.

Transfer function noise modelling of groundwater level fluctuation using threshold rainfall-based binary-weighted parameter estimation approach

ABSTRACTConsiderable uncertainty occurs in the parameter estimates of traditional rainfall–water level transfer function noise (TFN) models, especially with the models built using monthly time step datasets. This is due to the equal weights assigned for rainfall occurring during both water level rise and water level drop events while estimating the TFN model parameters using the least square technique. As an alternative to this approach, a threshold rainfall-based binary-weighted least square method was adopted to estimate the TFN model parameters. The efficacy of this binary-weighted approach in estimating the TFN model parameters was tested on 26 observation wells distributed across the Adyar River basin in Southern India. Model performance indices such as mean absolute error and coefficient of determination values showed that the proposed binary-weighted approach of fitting independent threshold-based TFN models for water level rise and water level drop scenarios considerably improves the model accuracy over other traditional TFN models.EDITOR D. KoutsoyiannisASSOCIATE EDITOR A. Fiori

검색 트래픽 정보를 활용한 고속도로 교통지표 분석 연구

Numerous research has been conducted using internet search data since the mid-2000s. For example, Google Inc. developed a service predicting influenza patterns using the internet search data. The main objective of this study is to prove the hypothesis that highway traffic indices are similar to the internet search patterns. In order to achieve this objective, a model to predict the number of vehicles entering the expressway and space-mean speed was developed and the goodness-of-fit of the model was assessed. The results revealed several findings. First, it was shown that the Google search traffic was a good predictor for the TCS entering traffic volume model at sites with frequent commute trips, and it had a negative correlation with the TCS entering traffic volume. Second, the Naver search traffic was utilized for the TCS entering traffic volume model at sites with numerous recreational trips, and it was positively correlated with the TCS entering traffic volume. Third, it was uncovered that the VDS speed had a negative relationship with the search traffic on the time series diagram. Lastly, it was concluded that the transfer function noise time series model showed the better goodness-of-fit compared to the other time series model. It is expected that Big Data from the internet search data can be extensively applied in the transportation field if the sources of search traffic, time difference and aggregation units are explored in the follow-up studies. Keywords big date; google trends; naver trend; TCS traffic/VDS speed; transfer function-noise model ; 빅 데이터; 구글 트렌드; 네이버 트렌드; TCS 교통량/VDS 속도; 전이함수 잡음 시계열 모형 Language: ko